We present a method for the calculation of the scattering states of a N+1th-particle coherently interacting with N correlated particles confined in a nanostructure and placed within an open domain. The method is based on a generalization of the quantum transmitting boundary method [C. Lent and D. Kirkner, J. App. Phys. 67, 6353 (1990)]. The antisymmetry conditions of the N+1-identical particles current-carrying state results from a proper choice of the boundary conditions. As an example which is relevant to coherent electronics, we apply the method to compute the exact transmission functions and phases of an electron crossing a 1D quantum dot with zero, one or two bound electrons.